A lackluster and seemingly uninterested City side was unable to break down the disciplined home side in a game of few chances that unsurprisingly ended in a goalless draw.
A clearly uninterested City side left much to be desired as the home side dominated the first half, with Pablo Hernandez and star striker Michu coming close to opening the scoring for the Swans early on.
City, aided by the introduction of Edin Dzeko, started the second half the stronger of the two sides and dominated possession for the vast majority of the final period but was unable to carve out any real chances on goal, and failed to seriously trouble a Swansea defense which had little trouble dealing with as uncharacteristically lackluster attacking performance.
Michael Laudrup made one change to the side that lost 2-0 to Chelsea last weekend, with Ki Sung-Yueng dropping to the bench to be replaced by Nathan Dyer.
Meanwhile, Roberto Mancini, whose side beat West Ham 2-1 last week, made two alterations, bringing in James Milner for Samir Nasri and Matija Nastasic for Joleon Lescott, whose wife went into labor shortly before kickoff.
With second place all but confirmed, City has seemingly let its foot off the gas somewhat as the season comes to a close, and Swansea - visibly desperate for its first league win in over two months as the club looks to ensure a top-half finish - took full advantage of that in the early stages.
Hernandez was handed the first real chance after quarter of an hour when he linked up with Nathan Dyer only to be let down by a disappointing finish, before Dyer was involved again five minutes later when his cross beat Nastasic and found Michu in front of goal, but his mishit volley flew wide.
Swansea's dominance and Manchester City's disinterest continued for the rest of the first half, with a multitude of chances raining down on the away defense and a consistently beleaguered Joe Hart, while the visiting side created very little at the other end.
Swansea's pressure culminated in a strong shout for a penalty with seven minutes of the first period left to play when Nastasic seemed to bundle over Michu in the center of the City penalty area. Despite the cries of outrage from everyone associated with Swansea, referee Mike Jones shook his head and allowed play to continue.
Clearly unimpressed with his side's effort in the first 45 minutes, Mancini brought on Dzeko for the second half, and the Bosnian had an immediate impact, improving a front line that had been lacking in ideas throughout the majority of the first half.
Despite dominating possession, City still found it difficult to carve out any clear chances against a resilient Swansea side, and last season's champion reverted to its old ways with 15 minutes left to play when the home side went on the front foot looking for a late winner.
However, after good play between Pablo Zabaleta and Carlos Tevez, Dzeko was set up with the perfect opportunity to steal all three points for City in the dying moments of the game. His close-range shot was skewed wide of the far post and left his side with no option but to share the points against a Swansea side that clearly wanted it more.